Quantum Gravity at Very High Energies

TL;DR

This paper investigates three-dimensional quantum gravity at high energies using path integral methods, revealing a connection to tensionless branes, classical singularities, and quantum suppression of the big bang, with implications for higher dimensions.

Contribution

It introduces a novel path integral approach to 3D quantum gravity, showing the effective dynamics as massless particles and analyzing the quantum behavior near singularities.

Findings

Exact solutions show singularities at t=0 indicating a big bang.

Quantum propagation amplitude vanishes as t approaches zero, implying quantum suppression of the big bang.

Results extend to higher dimensions (D>3).

Abstract

The problem of time and the quantization of three dimensional gravity in the strong coupling regime is studied following path integral methods. The time is identified with the volume of spacetime. We show that the effective action describes an infinite set of massless relativistic particles moving in a curved three-dimensional target space, i.e. a tensionless 3-brane on a curved background. If the cosmological constant is zero the target space is flat and there is no ` ` graviton" propagation (i.e., $G[g_{ij} (2), g_{ij} (1)] = 0$). If the cosmological constant is different from zero, 3D gravity is both classical and quantum mechanically soluble. Indeed, we find the following results: i) The general exact solutions of the Einstein equations are singular at $t=0$ showing the existence of a big-bang in this regime and ii) the propagation amplitude between two geometries $<g_{ij} (2), t_2| g_{ij} (1), t_1>$ vanishes as $t \to 0$, suggesting that big-bang is suppressed quantum mechanically. This result is also valid for $D>3$.